Actually, this isn't true, and it's one of the biggest stumbling blocks for learners of English.
The present perfect ("Have you sent the files?") is used to connect a past action with a present situation: "Have you sent the files?" means the same as, "Does the professor have the files now?"
That doesn't make any sense at all to me. The sending of files and the receiving of those files by the intended recipient are two completely different things and are separated by a time interval. Whether the files were sent by computer or by mail or by courier, there are reasons the recipient might not (yet) have received them. Furthermore, the sender, who is the person being asked the question, likely doesn't know if the recipient received the files (yet). ("have the files now")
And what if the professor did receive the files but then passed them on to someone else! In that scenario, the professor certainly would not "have the files now".
"Did you send the files?" and "Have you sent the files?" both only ask about the act of sending. ("past action") They have nothing to do with the "present situation".
Obviously there seems to be a difference between British and "American" English and that is unfortunate for English learners. Regardless of what kind of English is spoken, that English has to make sense and stand up to scrutiny. What rewboss said makes no sense to me, a person who is not British or American.
The past simple ("Did you send the files?") refers only to the action itself, and has no connection with the present at all.
With something as abstract as computer files, the difference is not clear, but consider this pair of sentences:
1..."the difference is not clear" ?? I thought you just disagreed with me for saying that the meanings were the same!
2...It doesn't matter what kind of files.
I wrote a letter.
I have written a letter.
The first sentence simply means that at some time in the past, I wrote a letter. Without any other context, it's not possible to say anything more than that. I think that applies to both sentences.
The second sentence means that right now, there exists in my possession a completed letter, ready to be posted. The focus is on the result of the writing, not the writing itself. I disagree.
Back to the original question, and in cases like this, where you are asking if somebody has recently performed a certain action, you can choose which tense you prefer to use. American speakers will prefer the past simple, while British speakers will usually use the present perfect.
Generally, if the connection with the present is clear from the context, or is made clear by a word like "already" or "just", Americans will use the past simple: But now you are suggesting that the meanings are the same.
I just sent it. (American English)
I've just sent it. (British English)